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Two Point Form of a Line

Question

Find the equation of the line that passes through the points $(7, 5)$ and $(- 9, 5)$
$y = 5$
$5 y = 7 x + 5$
$y = - 5$
$y = 5 x + 7$

A

5 y = 7 x + 5

B

y = 5

C

y = 5 x + 7

D

y = - 5

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Solution

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Since slope of line passing through two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
We now find the slope of the line passing through the points $(7, 5)$ and $(- 9, 5)$ as shown below:
$m = \frac{5 - 5}{- 9 - 7} = \frac{0}{- 16} = 0$
Therefore, the slope of the line is 0.
Now use the slope and either of the two points to find the $y$ -intercept.
$y = m x + b$
$5 = (0) (7) + b$
$b = 5$
Write the equation in slope intercept form as:
$y = m x + b$
$y = (0) x + 5$
$y = 5$
Hence, the equation of the line is $y = 5$ .

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